Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
388 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22581303 | C2 | semidirect |
| 3. #22581286 | C2 | semidirect |
| 4. #22581248 | C2 | semidirect |
| 5. #22581192 | C2 | semidirect |
| 6. #22581160 | C2 | semidirect |
| 7. #22581109 | C2 | semidirect |
| 8. C4×#14555775 | C2 | semidirect |
| 10. C2×#17984766 | C2 | semidirect |
| 92. D4×C139 | Q16 | semidirect |
| 122. C139 | #3299 | semidirect |
| 208. D4 | #14555775 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581660 | 2 |
| #22581303 | 2 |
| #22581286 | 2 |
| #22581248 | 2 |
| #22581192 | 2 |
| #22581160 | 2 |
| #22581109 | 2 |
| C4×#14555775 | 2 |
| D4×C139⋊C8 | 2 |
| C2×#17984766 | 2 |
| D4×Q8×C139 | 2 |
| #3299 | 139 |